What's the problem with Blair becoming a Catholic?
Some people have problems with Catholicism, either with the church policies, or with doctrinal questions, or with the notion of a political leader of one country being under the authority of a religious leader in another. But only a few people; not enough to matter.
Some people have problems with religion itself. But only a few people, indeed I suspect a majority of British politicians would confess one denomination or another.
Some people have problems with the fact that Blair, as Prime Minister, apparently had some kind of informal attachment to the Catholic Church, without making it public or official. Now we are getting closer to the issue, but by political standards of hypocrisy, this is still very minor stuff.
The real problem for the British is that to take religion so seriously that one would change denomination is just icky. It's OK to have a religion, but, as with a sausage, one shouldn't care or take too much notice of what's in it. That makes people uncomfortable. Part of that is a reasoned objection to the sort of behaviour that might result from taking religion seriously, but I think mostly it's just that worrying about the details of religion is in bad taste.
Even atheism is frowned on for the same reason. I previously held that one who does not positively believe in some specific idea of God should be considered an atheist, since they are not a theist. But I was wrong. The British distrust declared atheists, because atheists take religion too seriously. It's like being vegan, only worse -- there are, arguably, immediate practical justifications for veganism, but there is no practical justification for involving oneself in the details of religion to the extent necessary to call oneself an atheist. It is much more decent to just go along with whatever public aspects of religion fit one's social activities, while utterly ignoring any inner content, like everyone else does.
I've been moving in this direction a long time, but I think now I better understand why. I will in future be vaguely non-committal about my religion, because anything else shows poor taste.